RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1969, Volume 6, Issue 4, Pages 381–392 (Mi mz6944)

On group rings of abelian $p$-groups of any cardinality

S. D. Bermana, T. Zh. Mollovb

a Kharkov State University
b Plovdiv High Pedagogical Institute (Bulgaria)

Abstract: The problem is studied of the connection between an Abelian $p$-group $G$ of arbitrary cardinality and its group ring $LG$, where $L$ is a ring with unity nonzero characteristic $n\equiv0(\mod p)$, with $p$ being a prime. In particular, it is shown that group ring $LG$ defines to within isomorphism the basis subgroup of group $G$. If reduced Abelian $p$-group $G$ has finite type and if its Ulm factors decompose into direct products of cyclic groups, then group ring $LG$ determines group $G$ to within isomorphism.

Full text: PDF file (992 kB)

English version:
Mathematical Notes, 1969, 6:4, 686–692

Bibliographic databases:

UDC: 512.4

Citation: S. D. Berman, T. Zh. Mollov, “On group rings of abelian $p$-groups of any cardinality”, Mat. Zametki, 6:4 (1969), 381–392; Math. Notes, 6:4 (1969), 686–692

Citation in format AMSBIB
\Bibitem{BerMol69} \by S.~D.~Berman, T.~Zh.~Mollov \paper On group rings of abelian $p$-groups of any cardinality \jour Mat. Zametki \yr 1969 \vol 6 \issue 4 \pages 381--392 \mathnet{http://mi.mathnet.ru/mz6944} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=254155} \zmath{https://zbmath.org/?q=an:0204.35201|0187.29704} \transl \jour Math. Notes \yr 1969 \vol 6 \issue 4 \pages 686--692 \crossref{https://doi.org/10.1007/BF01093802}